Introduction

The magnetic properties exhibited in nanostructures made of just a few atoms are usually very different in comparison with the ones observed in bulk, surfaces, or thin-films (Bergman et al. 2016; Pianet et al. 2016; Cui et al. 2016; Singha et al. 2016; Li et al. 2016; Donati et al. 2016; Loth et al. 2012). In general, they are difficult to predict because they depend on countless number of factors such as chemical composition (Díaz-Sánchez et al. 2013), shape, size (Gruner et al. 2008), symmetry, magnetic ordering (Ruiz-Díaz et al. 2015), and interactions with its surroundings (Serrate et al. 2016), to name just a few. Nevertheless, there is currently a large number of cutting-edge experimental techniques which allow to characterize, manipulate, and fabricate magnetic nanostructures atom by atom from bottom-up approaches (Meier et al. 2008; Rau et al. 2014; Donati et al. 2014; Khajetoorians et al. 2012). From a fundamental perspective, the manipulation and control of these nanostructured materials allow us to study the underlying interactions that govern the magnetic phenomena at the atomic scale which are the essential ingredients to form the basis in the designing and developing of novel storage technologies with specific functionalities (Jungwirth et al. 2016; Loth et al. 2012; Khajetoorians et al. 2011).

In particular, transition-metal(TM)-based nanoparticles have been spotlighted due to a variety of technological applications(Sun et al. 2000; Yin et al. 2007; Sahoo et al. 2010). For instance, large magnetic anisotropy energies (MAEs) in small aggregates are often reported and it is of paramount importance bearing in mind that the MAE defines a preferential direction of magnetization and stabilizes such direction against temperature and external fields. The 3d-5d alloying is one of most widely used techniques for tuning the magnetic properties of small nanoparticles. It combines the large and stable magnetic moments of the strongly ferromagnetic 3d elements (e.g., Fe, Co, or Ni) with highly polarizable 5d elements such as Pt or Ir which often yields in a remarkable enhancement of the MAE in comparison with single-element compounds. For instance, combined theoretical and experimental works on relatively large-sized 3d-5d(4d) alloy core-shell clusters \(\sim \) 43–500 atoms in CoRh (Muñoz-Navia et al. 2009; Muñoz-Navia et al. 2009; Díaz-Sánchez et al. 2013) and FePt, CoPt nanoparticles \(\sim \) 13–920 atoms (Gruner et al. 2008; Gruner 2010) respectively have been highlighted the strong dependence of the magnetic properties on the chemical composition and cluster-shape. Altogether, enhanced anisotropies along with large orbital moments are remarked upon alloying for these binary compounds. Bimetallic compounds are also of great interest due to their lattice mismatch; strain-induced effects in core-shell nanoparticles have been reported which may play an important role into their local properties (Panizon and Ferrando 2016). For instance, core-shell morphologies have been produced experimentally to exploit the lattice strain to tune their chemical properties as in the case of PtCu-Pt nanoparticles (Strasser and Koh 2010).

In addition to varying the chemical composition to tune the electronic environment of the nanoalloys, there are alternative mechanisms which also allow to alter their electronic and magnetic properties. It is among the most popular approaches one can mention for instance the electric and magnetic field-assisted methods (Dasa et al. 2013, 2012; Hsu et al. 2017), being the former one of particular interest due to its local nature. However, this may involve the usage of external sources to generate such fields which is a clear disadvantage. Interestingly, a thoroughly used method in electrochemistry (Gleiter et al. 2001; Schnur and Groß 2011) but little exploited in the context of low-dimensional systems to tailor the local electronic properties is through the change in the carrier density or charge-doping. Recently, electron-doping has been proposed as a promising route to alter the magnetic properties of nanostructured materials in a controlled fashion. For instance, it has been shown that in ultra-thin multilayered systems (Ruiz-Díaz et al. 2013; Ruiz-Díaz and Stepanyuk 2014), the anisotropy is deeply modified upon electron(hole)-doping and triggers magnetization switching.

The objective of this work is to perform a first-principles calculations to investigate the impact of both chemical composition and charge-doping on the magnetic properties of TM binary nanoparticles taking CoPt core-shell alloys as prototypical examples. Notice that more complex configurations such as intermixing structures are also possible (Panizon and Ferrando 2016). Yet, our optimization procedure (initial core-shell like structures with no lattice mismatch only allows us to explore local minima, i.e., we exclude the possibility of taking into account other low-symmetry structures (Rossi et al. 2008; Barcaro et al. 2010). However, the validity and main conclusions regarding the influence of both chemical composition and charge doping on the magnetic properties of binary clusters will remain. Indeed, we demonstrate that the appropriate combination of 3d and 5d elements allows us to merge large moments with large MAEs. Moreover, charge-doping further stabilizes the MAE and boosts magnetization switching processes. The remainder of the paper is organized as follows: First, we highlight the main aspects regarding the theory and computations details used in the presented calculations. Later, we discuss the charge-doping effects and the impact of composition on the magnetic properties of CoPt core-shell alloys and correlate the MAE behavior with changes in the electronic structure of the clusters due to an enhancement of the spin-orbit interactions upon increasing the Pt-core-size. Finally, some general conclusions are outlined.

Computational details

The ground-state magnetic properties of the Co n Pt m core-shell alloy clusters are obtained in the framework of Hohenberg-Kohn-Sham’s density functional theory (DFT) (Hohenberg and Kohn 1964; Kohn and Sham 1965) as implemented in the Vienna Ab initio Simulation Package (VASP) (Kresse and Furthmüller 1996; Kresse and Hafner 1993). The spin-polarized Kohn-Sham (KS) equations (Kohn and Sham 1965) are solved in an augmented plane-wave basis set by using the projector augmented wave (PAW) method (Blöchl 1994; Kresse and Joubert 1999) within the supercell approach. For \(3d\)–5d TM binary alloys, the electronic and magnetic properties are accurately described by considering the \(5d\), \(5s\) and \(3d\), \(4s\), and \(4p\) electrons as valence states respectively (Blöchl 1994; Kresse and Joubert 1999). The exchange and correlation effects are treated in the generalized-gradient (GGA) (Parr and Yang 1989; Dreizler and Gross 1990) level by means of the Perdew-Wang exchange-correlation functional (PW91) (Perdew 1991). The clusters are placed inside of a simple cubic supercell whose dimensions are such that the interactions between neighboring images are negligible. In practice, this criterion is fulfilled when the images are separated from each other by at least 12 Å. The KS wave functions in the interstitial region are expanded in a plane wave basis set with a kinetic energy cut-off of 350 eV. Larger supercell sizes and higher cutoff energies were also tested yielding variations in the total energy less than 1 meV/per atom. Thus, the set of values chosen for supercell size and energy cutoff in the present work represent a good compromise between computational effort and accuracy. A modest Gaussian smearing (Mermin 1965) of the KS levels of 0.01 eV is introduced in order to improve the convergence and numerical stability. The energy calculations are carried out by considering only the \({\Gamma }\)-point in reciprocal space given that we are dealing with free-standing isolated clusters.

Structural optimization of Co n Pt m nanoparticles

The geometry optimization of the different Co n Pt m alloy clusters is performed by using the conjugate-gradient method until the forces on each atom are less than 5 meV/Å. The magnetic properties of the clusters are strongly dependent on the geometrical and chemical environment. Atomistic and DFT studies have predicted that in the case of core-shell nanoalloys, the lattice mismatch between elements induces a stress in the surface of the binary nanoparticles which leads in a reconstruction of the surface (Panizon and Ferrando 2016). In the case of CoPt nanoalloys, the lattice mismatch is meaningful. Typically, the nearest neighbour (NN) distance of pure-Co nanoparticles is around \(\mathrm {d}_{\text {NN}}\approx 2.3\)–2.5 Å while \(\mathrm {d}_{\text {NN}}\approx 2.6\)–2.8 Å for Pt-pure clusters. Thus, a careful global optimization is necessary to determine the true ground-state structure. In our study, the strain-induced effect in the restructuring of the surface is clearly observed in the case of the \(\text {Pt}_{19}\text {Co}_{66}\) structure (a Pt-core surrounded by a single Co-atomic layer shell in which one observes a complex structural distortion not only in the surface but in the atoms of the inner shell as well). The atoms located in the vertices of the quadrangular face (xy-plane) are compressed regarding the ones located in the vertices of the z-axis, generating an egg-like structure. The other considered CoPt morphologies (intermixed structures) also undergo non-trivial distortions. It is worthy to point out that such geometrical reconstruction breaks the overall symmetry of the structure suppressing the usual high-symmetry axes found in the conventional systems (e.g., cubic, hexagonal symmetry).

Since the magnetic degrees of freedom rise (existence of multiple magnetic configurations) when the number of atoms in the cluster increases, we consider a wide-range of possible collinear solutions as starting magnetic configurations having different spin arrangements for the cluster geometry optimizations. A structural optimization alongside with a systematic search of collinear magnetic solutions following a fixed-spin-moment procedure is performed by varying the total spin moment \(S_{z}\) of the cluster around some reasonable values \(N<S_{z}<3N\). Moreover, small random variations of the atomic positions and local moment orientations are introduced (non-collinear textures), which allows to test the stability of collinear solutions. The collinear spin-magnetic-moment configurations turned out to be the ground-state textures in all cases upon geometry and energy optimization.

Charge-doping and magnetocrystalline anisotropy

Once the ground-state structures of the Co n Pt m nanoparticles are obtained, we introduce a uniform charged-background inside of the supercell in order to simulate the charge-doping effect on the clusters (Ruiz-Díaz and Stepanyuk 2014). In practice, this can be achieved by varying the total number of valence electrons of the Co n Pt m nanoparticles. Typically, by adding(removing) one electron in the supercell with respect to the non-charged cluster (reference system) is enough for simulating a reasonable electron(hole)-doping. Clearly, the excess of charge(holes) causes the neutrality condition in the supercell to be broken. Thus, the excess of charge needs to be compensated by a constant background jellium to fulfill this constraint, otherwise the Coulomb energy would diverge (Gerstmann et al. 2003). This approach has been successfully applied in our previous works for ultra-thin multi-layered systems (Ruiz-Díaz et al. 2013; Ruiz-Díaz and Stepanyuk 2014). The magnetocrystalline anisotropy energy is a very sensitive quantity which requires to be treated with extreme care since for free-standing isolated clusters is usually of the order of just a few meV’s. In a second step, relativistic calculations taking into account the spin-orbit interaction are carried out with a much tight criterion in the electronic energy(ΔE = 10− 7 eV between two successive electronic steps). Such a strict criterion is crucial for calculating reliable MAEs. We rely on the magnetic force theorem (Bruno 1989) for determining the MAE of the clusters. Self-consistent calculations were also performed finding in both cases the same trends in the MAE behavior however. One should mention that the spin and orbital moments remain collinear between each other in both approaches (non-self and fully self-consistent relativistic calculations). We therefore focus our discussion mainly in the results obtained with the former approach.

Results and discussion

Non-charged CoPt clusters

We take as prototypical examples medium-sized CoPt octahedral-like core-shell alloy clusters having \(N=n+m = 85\) atoms and different core sizes, η c = N c /N = 0.23, 0.5, 0.72 and 1.0 where N c is the number of atoms in the core. The considered CoPt core-shell structures are sketched in Fig. 1. We begin our study by analyzing the role of the structural relaxations in the nanoparticles. In general, upon geometry optimization, the Co n Pt m alloys try to preserve their initial symmetry (octahedral symmetry) but noticeable distortions near the apexes are observed, specially in the case of \(\text {Pt}_{19}\text {Co}_{66}\) when an egg-like structure is formed. Only for the case of the pure Co-cluster (Co85), shorter inter-atomic distances are found in comparison to the nearest-neighbors distance in bulk [d = (2.35–2.44)Å; \(d^{Co}_{bulk}=\) 2.49Å]. For the CoPt alloys, the displayed inter-atomic distances are in the range of bulk distances \(d=\) (2.37-2.92)Å for Pt19Co66, \(d=\) (2.43-2.84)Å for Pt43Co42, and \(d=\) (2.49–2.77)Å for Pt61Co24 respectively. In order to get insights regarding the stability of the selected CoPt morphologies, we calculate the binding energy per atom (Ebin) in the canonical way: \(\mathrm {E}_{\text {bin}} = 1/\mathrm {N}\times (\mathrm {E}_{\text {tot}}-\text {nE}_{\text {Co}}-\text {mE}_{\text {Pt}})\) where \(\mathrm {N}= 85\), E t o t is the total energy of the cluster Co n Pt m and E C o (E P t ) is the energy of an single Co and Pt-atom respectively. We found \(\mathrm {E}_{\text {bin}}(\text {Co}_{85}) = -4.48\) eV, \(\mathrm {E}_{\text {bin}}(\text {Pt}_{19}\text {Co}_{66}) = -4.4\) eV, \(\mathrm {E}_{\text {bin}}(\text {Pt}_{43}\text {Co}_{42}) = -4.6\) eV, \(\mathrm {E}_{\text {bin}}(\text {Pt}_{61}\text {Co}_{24}) = -4.71\) eV. From such results, one concludes that the inter-mixed structures are lower in energy than that of the core-shell morphology. Even the pure Co-cluster (Co85) turned to be more stable than Pt19Co66. These results are in agreement with previous calculations using Monte Carlo and DFT methods for global optimization of structures in CoPt nanostructures which predict that the the intermixing is prefered for this kind of nanoalloys (Rossi et al. 2008; Barcaro et al. 2010).

Fig. 1
figure 1

(Color online) Illustration of the relaxed Co n Pt m octahedral-like core-shell alloy clusters having N = n + m = 85 atoms and different relative core sizes η c = N c /N, where N c is the number of atoms in the core. Light (pink) balls represent the Co atoms while dark (green) balls represent the Pt atoms

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Now that different Pt-Co intermixing substitutions are considered, the magnetic behavior is expected to be highly composition-dependent to the chemical order. In particular, we focus in striving to correlate the magnetocrystalline anisotropy with the chemical composition of the nanoparticle. Due to the symmetry of the selected clusters, the energy is calculated along the three highest symmetry magnetization directions (see Fig. 1), namely \(\delta =x,z\) and \(xy :=\{\phi =\pi /4,\theta =\pi /2\}\) for each considered core size, \(\eta _{c}\). As briefly discussed before, due to the lattice mismatch between Co and Pt, the structural distortions are considerable, breaking in this way the symmetry of the system. Therefore, the z and xy magnetization directions are non-equivalent otherwise this should be the case (i.e., perfect octahedral cluster). From these calculations, two magnetic anisotropy energies are obtained. An in-plane anisotropy which is the difference in energy between the xy and x directions, \({\Delta } \mathrm {E}_{\text {in}} =E_{xy}-E_{x}\) and an out-of-plane anisotropy defined by difference in energy between the z and x directions, \({\Delta } \mathrm {E}_{\text {out}} =E_{z}-E_{x}\) respectively. Owing to the symmetry of the considered clusters, we found that the out-of-plane MAEs are in general larger than the in-plane MAEs. For sake of sampling further the MAE behavior, an additional direction of magnetization was chosen. We take the \(xz :=\{\phi = 0,\theta =\pi /4\}\) direction, finding a considerable monotonous increasing of the MAE upon Pt-to-Co substitution. Defining now ΔE as \(E_{z} -E_{xz}\) , we obtain \({\Delta } \mathrm {E}= 0.41\), \(-\) 91.23, \(-\) 205.47, and \(-\) 332.6 meV for Co85, Pt19Co66, Pt43Co42 , and Pt61Co24 respectively. In order to get insights regarding the influence of the structural distortions on the MAE, we calculate as an example \({\Delta } \mathrm {E}_{\text {out}}\) for the non-distorted Pt19Co66 morphology assuming \(d=\) 2.68 Å between all the atoms. In this case, \({\Delta } \mathrm {E}_{\text {out}}\) is \(-\) 9.2 meV which is relative larger than that of the MAE of the optimized cluster (≈ 6 meV). In general, enhanced MAEs are observed in the non-distorted structures exhibiting that relaxations tend to reduce the MAE value.

We have obtained the energy along three different axes of quantization, the directions along the corner, center of edge and center of facet of the clusters; however, in order to determine the true hard axis or global minimum, one needs to calculate the energy in all the magnetization axes, namely E(ϕ,𝜃) which is beyond the scope of the present study. We mainly focus on the trends of the MAE as a function of the chemical composition and charge doping.

Moreover, the effect of the 3d-5d alloying on the MAE is exhibited since enhanced MAEs are obtained as the Pt-core-size increases (Pt-to-Co substitution.) We observe that among the considered Co n Pt m core-shell clusters, the pure Co-cluster(Co85) has a negligible (almost zero) MAE due to its small spin-orbit constant. In contrast, a non-trivial dependence of the MAE as a function of the Pt-concentration is observed. We found that the largest Pt-core-size cluster, \(\eta _{c}=\) 0.72 (Pt61Co24), possesses a remarkable large off-plan e MAE of \({\Delta } \mathrm {E}_{\text {out}}= -22.9\) meV. In the xy-plane, the easy-axis of magnetization is along the \(\delta =xy\) direction (ΔEin = − 23.6 meV). In addition, depending on the Pt-core-size, both in-plane(off-plane) directions of magnetization are identified as it can be seen in Fig. 2. Therefore, the strong chemical composition dependence on the magnetization direction is evidenced. The results show that this non-trivial MAE behavior renders impossible to a priori infer a clear trend of the MAE based only on the chemical composition of the cluster. This intricate behavior arises from the interplay of the local environment dependence and the corresponding enhancement of spin-orbit interactions.

Fig. 2
figure 2

(Color online) Calculated self-consistent (SC) and non-self-consistent (NSC) magnetocrystalline anisotropy energy of Co n Pt m core-shell clusters having N = n + m = 85 atoms and different core sizes η c . a Out-of plane anisotropy ΔE = E z − E x . b In-plane anisotropy ΔE = E x y − E x . The units are given in meV.

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We would like to comment in brief on the reliability of the approach used in calculating the MAEs. In general, the magnetic properties, in particular the MAE, are very sensitive to countless factors and certainly different levels of accuracy might yield to varied values. In order to quantify to some extend the robustness of the approach embraced in the present work, we compare both self-consistent and non-self consistent (magnetic force theorem) calculations for the non-charged clusters. We find that the general trends in the MAE behavior are preserved in all the considered cases (see Fig. 2). Thus, the magnetic properties of the charged CoPt clusters are discussed using the magnetic force theorem since we expect that the conclusions should remain the same.

In Table 1, the average magnetic spin and orbital moments as well as the corresponding local Co(Pt) moments for the different Co n Pt m core-shell alloy clusters are presented. In the pure Co-cluster (Co85), the average magnetic moment is modestly larger (\(\bar {\mu }= 1.78~\mu _{B}\)) than that in the bulk. On the other hand, although the average spin moment, \(\bar {\mu }\), of the cluster decreases as a whole when increasing the Pt-core-size from \(\eta _{c}= 0.23\) to 0.72, thanks to the increase of the contact with the Pt-atoms, the local spin moment of the Co atoms increases from 1.78 to 2.06 μ B . Consequently, owing to an enhancement in the hybridization of the Pt atoms, the induced spin moment slightly increases from 0.36 to 0.48 μ B . The orbital moments in the Co atoms are practically negligible regardless of the concentration of Pt in the cluster. Contrary, it is observed a dependence on the chemical composition of the nanoparticles in the orbital moments of the Pt atoms with small variations ranging from 0.01–0.2 μ B .

Table 1 Average spin(orbital) magnetic moments in core-shell Co n Pt m clusters having N= n + m = 85 atoms
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Charged CoPt clusters

The MAE in the CoPt alloys can be further altered by electron(hole)-doping. The excess(lack) of charge modifies the intra-atomic Coulomb repulsion that yields in a electronic redistribution affecting the MAE value. In between, such redistribution might also cause structural deformations in the nanoparticles. We found that in general such distortions are negligible for the considered electron(hole)-doping strength [1 electron(hole) per unit-cell]. Variations less than 2% in the interatomic distance with respect to the non-charge systems are observed. As in the case of the non-charged alloy nanoparticles, we calculate the energy of the clusters along the three highest symmetry axes as a function of the electron(hole)-doping strength. We start by discussing the results for the in-plane MAE (ΔEin = E x y -E x ) which are summarized in Fig. 3. Enhanced MAEs upon charge-doping are obtained in all the cases along with a non-monotonous MAE behavior as a function of function of the electron(hole)-doping strength. Interestingly, in the Co-rich nanoparticles regime (Co85 and Pt19Co66) magnetization switching is reveal (Fig. 3a–b). This is due to the relative small displayed in MAEs (∼ 0.1-1.5 meV) and under this scenario, the doping plays a key role over the competing weak magnetic interactions driven by the spin-orbit coupling. When increasing the Pt-concentration in the clusters, larger in MAEs are obtained (∼ 2.5 − 24 meV for \(\eta _{c}= 0.5\), 0.72) (Fig. 3c–d) and the magnetization switching mechanism is suppressed. Comparing our results, we can conclude that Co-to-Pt substitution promotes further stabilization mediated by the spin-orbit interactions.

Fig. 3
figure 3

(Color online) In-plane magnetocrystalline anisotropy ΔE = E x y − E x , as a function of the electron(hole) charge-doping of the considered Co n Pt m core-shell clusters having N = n + m = 85 atoms and different core sizes η c . The charge-doping scale (in units of e/unit cell) is referred to the neutral system. Positive (negative) values stand for an excess(lack) of valence electrons in the alloy cluster

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Let us move the discussion to the results regarding the off-plane MAE in the CoPt core-shell alloys. First of all, the same qualitative tendency (similar non-monotonous dependence of the MAE as a function of the charge-doping strength) is observed in the four considered clusters; however, the obtained MAEs are larger in comparison with the in-plane MAEs previously discussed. Nonetheless, the spin-orbit constant for Co is small and the Co85 displays a modest in-plane MAE (neutral system); however, the changes in the MAE behavior are noticeable upon the doping. The non-charged cluster has a very small in-plane anisotropy (close to zero), so it is expected that small variations in the electronic environment will produce reversal magnetization. The easy-axis of magnetization happens to be out of plane, along the z-axis upon charge injection and becomes more stable as the charge doping strength increases. The anisotropy further stabilizes reaching values around 0.7 meV for 1e/unit-cell. Contrary, it would appear that the initial weak in-plane MAE is restored and shows a linear behavior upon hole injection (see Fig. 4a). Its value is roughly constant nearly 0.1 meV with hardly appreciable variations.

A more complicated behavior is found in the CoPt core-shell alloys since there is no clear trend of a preferred direction of magnetization. Both Co-rich and Pt-rich concentrations (η c = 0.23 and 0.73) display remarkable large off-plane MAEs exhibiting values ranging from 17 to 25 meV upon electron-doping (see Fig. 4b–d). Only in case where the ratio between the number of Co and Pt atoms is the same (η c ∼ 0.5), the nanoparticle has a relative small in-plane MAE ranging from 2.5 to 3.5 meV (see Fig. 4c). Intriguingly, for any of the studied CoPt core-shell alloys, no evidence of reversal magnetization was observed. It can be attributed to the relative large \({\Delta } \mathrm {E}_{\text {out}}\) values evidencing the robustness of the magnetization direction ruled by the large spin-orbit interactions.

Given that the magnetocrystalline anisotropy mainly arises from the spin-orbit interactions, it is expected that there is a correlation between the MAE and orbital moments. Thus, as a first approach to endeavor quantifying the charge-doping effects on the MAE, we analyze the orbital moment behavior as a function of the charge-doping strength. We choose Pt19Co66 as an example since this cluster shows a non-monotonous as well as smooth MAE behavior upon doping. In Fig. 5a–b, we present the total orbital moment of the cluster alloy for the three considered directions of magnetization \(\delta = x,xy\), and z respectively. It can be appreciated that the orbital moment along the z-axis remains roughly constant approximately \({\mu ^{z}_{L}}= 7.8~\mu _{B}\) for hole injection which is consistent with the observed small variations in the off-plane MAE, (ΔEout = E z − E x ) around 5–7 meV. Unlike, upon charge-doping, the orbital moment rises which is reflected by a meaningful increase of the anisotropy from \({\Delta } E_{out}\)\(\sim \) 5 to 17 meV (Fig. 4b). Similar conclusions can be deduced when comparing \({\Delta } E_{in}=E_{xy}\)-E x and \(\mu ^{x,xy}_{L}\). These results evidence that a change in MAE can be associated with a change in the orbital moment resembling the Bruno’s relation for explaining the MAE origins (Bruno 1989). In Fig. 5c, we plot the orbital off-plane anisotropy, \({\Delta } \mu ^{zx}_{L}= {\mu ^{z}_{L}}-{\mu ^{x}_{L}}\) as a function of the charge(hole)-doping strength. Indeed, when \({\Delta } \mu ^{zx}_{L}\) raises, \({\Delta } E_{out}\) also increases and vice-versa.

Fig. 4
figure 4

(Color online) Off-plane magnetocrystalline anisotropy ΔE = E z − E x , as a function of the electron(hole) charge-doping of the considered Co n Pt m core-shell clusters having N = n + m = 85 atoms and different core sizes η c . The charge-doping scale (in units of e/unit cell) is referred to the neutral system. Positive (negative) values stand for an excess(lack) of valence electrons in the cluster

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Fig. 5
figure 5

(Color online) Total orbital magnetic moment \(\mu _{L}={\sum }^{N}_{i = 1}\mu ^{\delta }_{i}\), for the Pt19Co66 core-shell cluster as a function of the electron(hole) charge-doping. Positive (negative) values stand for an excess(lack) of valence electrons in the cluster. The charge-doping scale (in units of e/unit cell) is referred to the neutral system. a Total orbital magnetic moment along the z\(\mu _{L}={\sum }^{N}_{i = 1}{\mu ^{z}_{i}}\), direction according to Fig. 1. b Total orbital magnetic moments along δ = x and xy\(\mu _{L}={\sum }^{N}_{i = 1}\mu ^{x,xy}_{i}\), respectively. c Total out-of plane orbital anisotropy, \({\Delta } \mu ^{zx}_{L} = {\mu ^{z}_{L}}-{\mu ^{x}_{L}}\). The units are given in μ B

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Electronic structure of the CoPt alloy clusters

A simple and fashionable way to elucidate major insights regarding the microscopy origins of the MAE behavior of the CoPt alloy clusters from a local perspective is to assess the prevailing contributions to the magnetocrystalline anisotropy driven by the coupling of the different d-orbitals with the spin-orbit angular-momentum operators. Resorting to the second-order perturbation approach (Wang et al. 1993)

$$ \text{MAE}= \mathrm{E}_{\mathrm{z}}-\mathrm{E}_{\mathrm{x}} \!\sim\! \xi^{2} \sum\limits_{o,u} \!\frac{|{\kern-.5pt} \langle \psi_{u}| l_{z} |\psi_{o} \rangle{\kern-.5pt} |^{2} \,-\, |{\kern-.5pt} \langle \psi_{u}| l_{x}|\psi_{o} \rangle{\kern-.5pt} |^{2} } {\epsilon_{u}\,-\,\epsilon_{o}} $$
(1)

where \(\{ \psi _{o},\psi _{u}\}\) refer to the unoccupied (occupied) states and \(\{ l_{x} , l_{z}\}\) the angular momentum operators respectively and ξ is the spin-orbit constant. It is straightforward to infer that the predominant contributions to the MAE arise from the states near to the Fermi level and its behavior is essentially ruled by the denominator in Eq. 1. Furthermore, since the majority d-band for the Co and Pt elements are fully occupied, the spin-flip between the up- and down-states is suppressed and the MAE behavior can be associated to the coupling between states in the minority d-band only. Depending on the symmetry of the d-orbitals, the coupling between the different occupied and unoccupied states via the spin-orbit angular-momentum operators, a particular direction of magnetization is preferred according to Table 2 (Dasa et al. 2013; Ruiz-Díaz et al. 2015). The interplay between all the couplings determines the easy-axis of magnetization of the cluster. In Fig. 6, the minority d-orbital-resolved density of states (DOS) for the Co n Pt m core-shell alloy clusters around the Fermi level is plotted . After analyzing the spin-orbit coupling matrix elements between the different d-orbitals along with the DOS profile (DOS ∝〈ψ u ||ψ o 〉2), one can observed that for Co85, there is a depletion of the d-orbitals near the Fermi energy (see Fig. 6) which indicates a weak coupling between the occupied and unoccupied states yielding therefore in a negligible MAE as it was previously discussed. Contrary, the large off-plane(in-plane) MAE found for the Pt61Co24 alloy cluster(∼ 26 meV) can be easily understood by the substantial enhancement of the coupling mainly between the \(d_{xy}\) and \(d_{x^{2}-y^{2}}\) orbitals and \(d_{xz}\) and \(d_{x^{2}-y^{2}}\), which can be envisaged by the large number of of states of these orbitals around the Fermi level that favors an off-plane(in-plane) direction of magnetization respectively. The obtained intermediate MAE values (∼ 2–15 meV) for the Pt19Co66 and Pt43Co42 are also reflected in the profile of the DOS for these clusters. The strength of the different off-plane(in-plane) couplings (states near the Fermi energy) are between the couplings for Co85 and Pt61Co24. One can see thus that the magnetocrystalline anisotropy is driven by the spin-orbit interactions and it has a profound impact in the electronic structure of the clusters which can be traced back in the density of states.

Table 2 Couplings between the occupied (unoccupied) states depending on the d-orbital symmetry and their contribution to the direction of magnetization
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Fig. 6
figure 6

(Color online) Minority d-orbital-resolved density of states(DOS) for the Co n Pt m core-shell alloy clusters around the Fermi level

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Conclusions

The magnetic properties of CoPt core-shell alloy nanoparticles have been investigated in the framework of density functional theory. Our results demonstrate that tuning the chemical composition, in particular by 3d-5d alloying and simultaneously varying their concentration has a profound impact in cluster magnetism. Remarkably, charge-doping offers an appealing route for further tailoring the magnetic properties of the cluster alloys. Our results show that this mechanism promotes further stabilization in the direction of magnetization which is appealing for instance in magnetic recording. More intriguing is that the magnetization switching processes may also be triggered. Finally, the microscopical basis of the magnetocrystalline anisotropy of the CoPt alloy clusters is associated with changes in their electronic structure and the MAE behavior can be explained qualitatively.